dsp.FFT System object

Package: dsp

Discrete Fourier transform

Description

The FFT object computes the discrete Fourier transform (DFT) of an input. The object uses one or more of the following fast Fourier transform (FFT) algorithms depending on the complexity of the input and whether the output is in linear or bit-reversed order:

  • Double-signal algorithm

  • Half-length algorithm

  • Radix-2 decimation-in-time (DIT) algorithm

  • Radix-2 decimation-in-frequency (DIF) algorithm

  • An algorithm chosen by FFTW [1], [2]

To compute the DFT of an input:

  1. Define and set up your FFT object. See Construction.

  2. Call step to compute the DFT of the input according to the properties of dsp.FFT. The behavior of step is specific to each object in the toolbox.

Construction

H = dsp.FFT returns a FFT object, H, that computes the DFT of an N-D array. For column vectors or multidimensional arrays, the FFT object computes the DFT along the first dimension. If the input is a row vector, the FFT object computes a row of single-sample DFTs and issues a warning.

H = dsp.FFT('PropertyName',PropertyValue, ...) returns a FFT object, H, with each property set to the specified value.

Properties

FFTImplementation

FFT implementation

Specify the implementation used for the FFT as one of Auto | Radix-2 | FFTW. When you set this property to Radix-2, the FFT length must be a power of two.

BitReversedOutput

Order of output elements relative to input elements

Designate order of output channel elements relative to order of input elements. Set this property to true to output the frequency indices in bit-reversed order. The default is false, which corresponds to a linear ordering of frequency indices.

Normalize

Divide butterfly outputs by two

Set this property to true if the output of the FFT should be divided by the FFT length. This option is useful when you want the output of the FFT to stay in the same amplitude range as its input. This is particularly useful when working with fixed-point data types.

The default value of this property is false with no scaling.

FFTLengthSource

Source of FFT length

Specify how to determine the FFT length as Auto or Property. When you set this property to Auto, the FFT length equals the number of rows of the input signal. The default is Auto.

FFTLength

FFT length

Specify the FFT length. This property applies when you set the FFTLengthSource property to Property. The default is 64.

This property must be a power of two when the input is a fixed-point data type, or when you set the BitReversedOutput property to true, or when you set the FFTImplementation property to Radix-2.

WrapInput

Boolean value of wrapping or truncating input

Wrap input data when FFT length is shorter than input length. If this property is set to true, modulo-length data wrapping occurs before the FFT operation, given FFT length is shorter than the input length. If this property is set to false, truncation of the input data to the FFT length occurs before the FFT operation. The default is true.

 Fixed-Point Properties

Methods

cloneCreate FFT object with same property values
getNumInputsNumber of expected inputs to step method
getNumOutputsNumber of outputs of step method
isLockedLocked status for input attributes and nontunable properties
releaseAllow property value and input characteristics changes
stepDiscrete Fourier transform of input

Examples

Find frequency components of a signal in additive noise:

 Fs = 800; L = 1000; 
 t = (0:L-1)'/Fs; 
 x = sin(2*pi*250*t) + 0.75*cos(2*pi*340*t); 
 y = x + .5*randn(size(x)); % noisy signal
 
hfft = dsp.FFT('FFTLengthSource', 'Property', ...
 'FFTLength', 1024);

 Y = step(hfft, y);

 % Plot the single-sided amplitude spectrum
 plot(Fs/2*linspace(0,1,512), 2*abs(Y(1:512)/1024));
 title('Single-sided amplitude spectrum of noisy signal y(t)');
 xlabel('Frequency (Hz)'); ylabel('|Y(f)|'); 

Algorithms

This object implements the algorithm, inputs, and outputs described on the FFT block reference page. The object properties correspond to the block parameters.

References

[1] FFTW (http://www.fftw.org)

[2] Frigo, M. and S. G. Johnson, "FFTW: An Adaptive Software Architecture for the FFT,"Proceedings of the International Conference on Acoustics, Speech, and Signal Processing, Vol. 3, 1998, pp. 1381-1384.

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